f(x)=(x+3)(x-3)(x+2)(x-1)(x+2i)(x-2i)

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Solution for f(x)=(x+3)(x-3)(x+2)(x-1)(x+2i)(x-2i) equation: 


Simplifying
f(x) = (x + 3)(x + -3)(x + 2)(x + -1)(x + 2i)(x + -2i)

Multiply f * x
fx = (x + 3)(x + -3)(x + 2)(x + -1)(x + 2i)(x + -2i)

Reorder the terms:
fx = (3 + x)(x + -3)(x + 2)(x + -1)(x + 2i)(x + -2i)

Reorder the terms:
fx = (3 + x)(-3 + x)(x + 2)(x + -1)(x + 2i)(x + -2i)

Reorder the terms:
fx = (3 + x)(-3 + x)(2 + x)(x + -1)(x + 2i)(x + -2i)

Reorder the terms:
fx = (3 + x)(-3 + x)(2 + x)(-1 + x)(x + 2i)(x + -2i)

Reorder the terms:
fx = (3 + x)(-3 + x)(2 + x)(-1 + x)(2i + x)(x + -2i)

Reorder the terms:
fx = (3 + x)(-3 + x)(2 + x)(-1 + x)(2i + x)(-2i + x)

Multiply (3 + x) * (-3 + x)
fx = (3(-3 + x) + x(-3 + x))(2 + x)(-1 + x)(2i + x)(-2i + x)
fx = ((-3 * 3 + x * 3) + x(-3 + x))(2 + x)(-1 + x)(2i + x)(-2i + x)
fx = ((-9 + 3x) + x(-3 + x))(2 + x)(-1 + x)(2i + x)(-2i + x)
fx = (-9 + 3x + (-3 * x + x * x))(2 + x)(-1 + x)(2i + x)(-2i + x)
fx = (-9 + 3x + (-3x + x2))(2 + x)(-1 + x)(2i + x)(-2i + x)

Combine like terms: 3x + -3x = 0
fx = (-9 + 0 + x2)(2 + x)(-1 + x)(2i + x)(-2i + x)
fx = (-9 + x2)(2 + x)(-1 + x)(2i + x)(-2i + x)

Multiply (-9 + x2) * (2 + x)
fx = (-9(2 + x) + x2(2 + x))(-1 + x)(2i + x)(-2i + x)
fx = ((2 * -9 + x * -9) + x2(2 + x))(-1 + x)(2i + x)(-2i + x)
fx = ((-18 + -9x) + x2(2 + x))(-1 + x)(2i + x)(-2i + x)
fx = (-18 + -9x + (2 * x2 + x * x2))(-1 + x)(2i + x)(-2i + x)
fx = (-18 + -9x + (2x2 + x3))(-1 + x)(2i + x)(-2i + x)
fx = (-18 + -9x + 2x2 + x3)(-1 + x)(2i + x)(-2i + x)

Multiply (-18 + -9x + 2x2 + x3) * (-1 + x)
fx = (-18(-1 + x) + -9x * (-1 + x) + 2x2 * (-1 + x) + x3(-1 + x))(2i + x)(-2i + x)
fx = ((-1 * -18 + x * -18) + -9x * (-1 + x) + 2x2 * (-1 + x) + x3(-1 + x))(2i + x)(-2i + x)
fx = ((18 + -18x) + -9x * (-1 + x) + 2x2 * (-1 + x) + x3(-1 + x))(2i + x)(-2i + x)
fx = (18 + -18x + (-1 * -9x + x * -9x) + 2x2 * (-1 + x) + x3(-1 + x))(2i + x)(-2i + x)
fx = (18 + -18x + (9x + -9x2) + 2x2 * (-1 + x) + x3(-1 + x))(2i + x)(-2i + x)
fx = (18 + -18x + 9x + -9x2 + (-1 * 2x2 + x * 2x2) + x3(-1 + x))(2i + x)(-2i + x)
fx = (18 + -18x + 9x + -9x2 + (-2x2 + 2x3) + x3(-1 + x))(2i + x)(-2i + x)
fx = (18 + -18x + 9x + -9x2 + -2x2 + 2x3 + (-1 * x3 + x * x3))(2i + x)(-2i + x)
fx = (18 + -18x + 9x + -9x2 + -2x2 + 2x3 + (-1x3 + x4))(2i + x)(-2i + x)

Combine like terms: -18x + 9x = -9x
fx = (18 + -9x + -9x2 + -2x2 + 2x3 + -1x3 + x4)(2i + x)(-2i + x)

Combine like terms: -9x2 + -2x2 = -11x2
fx = (18 + -9x + -11x2 + 2x3 + -1x3 + x4)(2i + x)(-2i + x)

Combine like terms: 2x3 + -1x3 = 1x3
fx = (18 + -9x + -11x2 + 1x3 + x4)(2i + x)(-2i + x)

Multiply (18 + -9x + -11x2 + 1x3 + x4) * (2i + x)
fx = (18(2i + x) + -9x * (2i + x) + -11x2 * (2i + x) + 1x3 * (2i + x) + x4(2i + x))(-2i + x)
fx = ((2i * 18 + x * 18) + -9x * (2i + x) + -11x2 * (2i + x) + 1x3 * (2i + x) + x4(2i + x))(-2i + x)
fx = ((36i + 18x) + -9x * (2i + x) + -11x2 * (2i + x) + 1x3 * (2i + x) + x4(2i + x))(-2i + x)
fx = (36i + 18x + (2i * -9x + x * -9x) + -11x2 * (2i + x) + 1x3 * (2i + x) + x4(2i + x))(-2i + x)
fx = (36i + 18x + (-18ix + -9x2) + -11x2 * (2i + x) + 1x3 * (2i + x) + x4(2i + x))(-2i + x)
fx = (36i + 18x + -18ix + -9x2 + (2i * -11x2 + x * -11x2) + 1x3 * (2i + x) + x4(2i + x))(-2i + x)
fx = (36i + 18x + -18ix + -9x2 + (-22ix2 + -11x3) + 1x3 * (2i + x) + x4(2i + x))(-2i + x)
fx = (36i + 18x + -18ix + -9x2 + -22ix2 + -11x3 + (2i * 1x3 + x * 1x3) + x4(2i + x))(-2i + x)
fx = (36i + 18x + -18ix + -9x2 + -22ix2 + -11x3 + (2ix3 + 1x4) + x4(2i + x))(-2i + x)
fx = (36i + 18x + -18ix + -9x2 + -22ix2 + -11x3 + 2ix3 + 1x4 + (2i * x4 + x * x4))(-2i + x)
fx = (36i + 18x + -18ix + -9x2 + -22ix2 + -11x3 + 2ix3 + 1x4 + (2ix4 + x5))(-2i + x)

Reorder the terms:
fx = (36i + -18ix + -22ix2 + 2ix3 + 2ix4 + 18x + -9x2 + -11x3 + 1x4 + x5)(-2i + x)
fx = (36i + -18ix + -22ix2 + 2ix3 + 2ix4 + 18x + -9x2 + -11x3 + 1x4 + x5)(-2i + x)

Multiply (36i + -18ix + -22ix2 + 2ix3 + 2ix4 + 18x + -9x2 + -11x3 + 1x4 + x5) * (-2i + x)
fx = (36i * (-2i + x) + -18ix * (-2i + x) + -22ix2 * (-2i + x) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = ((-2i * 36i + x * 36i) + -18ix * (-2i + x) + -22ix2 * (-2i + x) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))

Reorder the terms:
fx = ((36ix + -72i2) + -18ix * (-2i + x) + -22ix2 * (-2i + x) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = ((36ix + -72i2) + -18ix * (-2i + x) + -22ix2 * (-2i + x) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + (-2i * -18ix + x * -18ix) + -22ix2 * (-2i + x) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))

Reorder the terms:
fx = (36ix + -72i2 + (-18ix2 + 36i2x) + -22ix2 * (-2i + x) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + (-18ix2 + 36i2x) + -22ix2 * (-2i + x) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + (-2i * -22ix2 + x * -22ix2) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))

Reorder the terms:
fx = (36ix + -72i2 + -18ix2 + 36i2x + (-22ix3 + 44i2x2) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + (-22ix3 + 44i2x2) + 2ix3 * (-2i + x) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + (-2i * 2ix3 + x * 2ix3) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))

Reorder the terms:
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + (2ix4 + -4i2x3) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + (2ix4 + -4i2x3) + 2ix4 * (-2i + x) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + (-2i * 2ix4 + x * 2ix4) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))

Reorder the terms:
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + (2ix5 + -4i2x4) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + (2ix5 + -4i2x4) + 18x * (-2i + x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + (-2i * 18x + x * 18x) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + (-36ix + 18x2) + -9x2 * (-2i + x) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + -36ix + 18x2 + (-2i * -9x2 + x * -9x2) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + -36ix + 18x2 + (18ix2 + -9x3) + -11x3 * (-2i + x) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + -36ix + 18x2 + 18ix2 + -9x3 + (-2i * -11x3 + x * -11x3) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + -36ix + 18x2 + 18ix2 + -9x3 + (22ix3 + -11x4) + 1x4 * (-2i + x) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + -36ix + 18x2 + 18ix2 + -9x3 + 22ix3 + -11x4 + (-2i * 1x4 + x * 1x4) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + -36ix + 18x2 + 18ix2 + -9x3 + 22ix3 + -11x4 + (-2ix4 + 1x5) + x5(-2i + x))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + -36ix + 18x2 + 18ix2 + -9x3 + 22ix3 + -11x4 + -2ix4 + 1x5 + (-2i * x5 + x * x5))
fx = (36ix + -72i2 + -18ix2 + 36i2x + -22ix3 + 44i2x2 + 2ix4 + -4i2x3 + 2ix5 + -4i2x4 + -36ix + 18x2 + 18ix2 + -9x3 + 22ix3 + -11x4 + -2ix4 + 1x5 + (-2ix5 + x6))

Reorder the terms:
fx = (36ix + -36ix + -18ix2 + 18ix2 + -22ix3 + 22ix3 + 2ix4 + -2ix4 + 2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)

Combine like terms: 36ix + -36ix = 0
fx = (0 + -18ix2 + 18ix2 + -22ix3 + 22ix3 + 2ix4 + -2ix4 + 2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)
fx = (-18ix2 + 18ix2 + -22ix3 + 22ix3 + 2ix4 + -2ix4 + 2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)

Combine like terms: -18ix2 + 18ix2 = 0
fx = (0 + -22ix3 + 22ix3 + 2ix4 + -2ix4 + 2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)
fx = (-22ix3 + 22ix3 + 2ix4 + -2ix4 + 2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)

Combine like terms: -22ix3 + 22ix3 = 0
fx = (0 + 2ix4 + -2ix4 + 2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)
fx = (2ix4 + -2ix4 + 2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)

Combine like terms: 2ix4 + -2ix4 = 0
fx = (0 + 2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)
fx = (2ix5 + -2ix5 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)

Combine like terms: 2ix5 + -2ix5 = 0
fx = (0 + -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)
fx = (-72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6)

Solving
fx = -72i2 + 36i2x + 44i2x2 + -4i2x3 + -4i2x4 + 18x2 + -9x3 + -11x4 + 1x5 + x6

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.
f = -72i2x-1 + 36i2 + 44i2x + -4i2x2 + -4i2x3 + 18x + -9x2 + -11x3 + x4 + x5

Simplifying
f = -72i2x-1 + 36i2 + 44i2x + -4i2x2 + -4i2x3 + 18x + -9x2 + -11x3 + x4 + x5

Reorder the terms:
f = 36i2 + -72i2x-1 + 44i2x + -4i2x2 + -4i2x3 + 18x + -9x2 + -11x3 + x4 + x5

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